$1.$ a$)$ Bara enterprises operates in Kitale town. On annual basis, it orders $480,000$ pens form a Nairobi based distributor. A packet of $24$ pens delivered to Baras warehouse cost sh $480$ including transport charges. The supermarket barrows money from ABC bank of an interest rate of $10\%$ p$.$a to finance its inventories. The supermarket also incurs sh $1,500$ to place an order for the pens and sh $8$ carrying cost for each pen

REQUIRED:

i$)$ Calculate the economic order quantity $($EOQ$)$ for the pens

ii$)$ Total cost of the EOQ.

iii$)$ For orders for $72,000$ pens and above the distributer has offered a discount rate of $10\%$ on delivery price.

Advice the management of the supermarket on whether to take advantages of the discount offer. $(6$ Marks$)$